We like banana popsicles I have a few mini ice cube trays the ice cubes are tiny squares.
So I fill one tray with sugar water the other with sprite.
We start with these things 1'st as plain water always comes back up.

The sprite is good for smaller kids as it doesn't freeze solid like water the carbonation makes it flake apart because of the air bubbles.
I kinda smash them up in spoons and spoon feed them it.

Food we start slow with saltines, then chicken noodle soup I cut up the noodles plus break up the chunks of chicken. I have found that after being sick my kids do not chew their food and that can make for more vomiting.
Banana's, plain toast, rice, apple sauce is also things they are offered right after the crackers stay down, they usually want soup though..

As for keeping things easier when vomit gets on them I put down towels over pillows, beds use them for blankets and cover the ground by their beds.
I find them easier to shake out than sheets.
Even though I give them a barf bowl or trash can they still get sick everywhere.
I also put them on the floor since carpet is harder to clean.
So basically its towels every where lol.
Heathly kids are to stay out of where the sick kids are easier said than done other though.